PLIEGO DE CONDICIONES OBRA CIVIL
2. PLIEGO DE CONDICIONES TECNICAS ESPECÍFICAS
2.4. ALBAÑILERIA
−`2 2t
.
Under this model, the rate of cooperation decreases gradually over time, in line with the experimental results of Figure 10(a) without delay. (The initial increase in cooperation rates in the fast treatments is likely due to subjects reacting relatively slowly to adjusting their action from the end of the previous block.) Of course, a richer model of passage times and cutoff strategies can be used to fit the data precisely by fitting an appropriate inverse Gaussian distribution to average cooperation rates and allowing for variation in thresholds `.
3.6 Discussion
Our experiments provide the first systematic treatment of delay, communication, and reaction lags in a repeated game with frequent actions and imperfect monitoring.
The results draw attention to several discrepancies with standard theory. The first finding is that delay unambiguously hurt subjects. This is at odds with the Abreu et al.(1991) argument that information delay can substantially help players to re-duce the likelihood of inefficient punishments. The argument is robust—it holds in games with frequent and infrequent actions, with unbounded patience, even in ap-proximate equilibrium, which makes the empirical finding all the more puzzling. One explanation of it is that delay makes it more difficult for subjects to learn the kind of opponent they are facing. Intuitively, if subjects face too much uncertainty over their opponents’ planned behavior, then it may be difficult to justify cooperating with them. The absence of delay may help players to signal their intended behavior more effectively.
Our second finding is that communication unambiguously helps subjects. Al-though it is well known in the experimental literature that communication generally improves welfare in a wide variety of strategic contexts, there is no strong theoretical justification for it adding (or subtracting) value in our experiment, unless—again—it helps to reduce subjects’ uncertainty over their opponents’ intentions. This suggests several sources of possible gains from reducing uncertainty over opponents’ strategies.
First, it may motivate a subject to cooperate more if she is more confident that her opponent is likely to cooperate in return. Second, it may be easier to give incentives for cooperation to opponents if they can be made better aware of the consequences of their defection. In treatments with communication, where subjects announce their contingent plans at the beginning of every block, both of these channels should be facilitated—at least somewhat–and we find this to be the case. Subjects use messages to inform their opponents of future strategies, and reported and actual behaviors are significantly aligned.
We also find little evidence that reaction lags affect behavior in our experiment.
This is a notable observation in light of the experiments reported in Friedman and Oprea (2012), where cooperation rates increase monotonically as players are given the opportunity to respond more quickly. Friedman and Oprea (2012) argued that response lags prevent players from quickly punishing deviations and that the gains to shorter lags are monotonic. Crucially, this argument only makes sense with perfect monitoring. In an environment like ours where information is noisy, reaction lags may allow players to gain a better idea of whether their partners are being cooperative, thereby supporting more efficient equilibria. We find, however, that cooperation does not seem to be affected in practice by how much time a player has to respond to a
signal.
Our instrumental variable-based estimation shows that subjects behavior is driven by observations of the public signal. Using an opponent’s strategic behavior as an instrument is justified by the assumption that subjects play mixed strategies. As a result, conditional on the public signal, random changes in a subject’s behavior must be mutually independent. Since the coefficient on the public signal is estimated with an instrument, it is unbiased regardless of other omitted variables. If there are no omitted variables then the regression equation is consistent with a first-order approximation of public strategies. Of course, if we assume that subjects’ behavior is consistent with equilibrium then players must be playing public equilibria. From a practical point of view, public equilibrium makes testable restrictions on feasible outcomes, such as the welfare bound of Proposition 1. However, our treatment with communication implies that the public equilibrium bound is violated. This could be for several reasons. First, it could be that subjects simply do not play equilibrium strategies. However, if the equilibrium assumption is dropped then it is not clear what structural predictions can be made. Secondly, it could be that their bounded rationality means that they are incapable of playing public equilibria, as they cannot react immediately to an individual bad news event. This may improve welfare, as illustrated in Section 3.4.4. However, it is not clear why players would exploit this bounded rationality in treatments with communication in order to exceed the pub-lic equilibrium bound but not in those without. Thirdly, subjects may be playing private—not public—strategies. From a technical point of view, public equilibrium is an assumption that often puts severe restrictions on behavior. That is, it precludes players from certain behavior that may be intuitively justified in some contexts.
Rahman (2012, 2013a) explores this issue at some length and argues that public equilibria preclude secret monitoring and infrequent coordination amongst players.
Both of these behaviors have the potential to improve their welfare significantly, so much so that the impossibility results of Sannikov and Skrzypacz (2007, 2010) can be completely overturned. Our interest in future work is to explore experimentally how infrequent coordination can help sustain cooperation in the laboratory.
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